3.427   ODE No. 427

$$\boxed{{\displaystyle (3x+5){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-(3y\left(x\right)+x)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+y\left(x\right)=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.634581 (sec), leaf count = 479 $$\{\{y(x)\to \frac{-\sqrt{5}\sqrt{-144e^{\frac{4c_1}{3}}{x}^2-360e^{\frac{4c_1}{3}}x+24e^{\frac{8c_1}{3}}x-225e^{\frac{4c_1}{3}}+30e^{\frac{8c_1}{3}}-e^{4c_1}}+6e^{\frac{4c_1}{3}}x+15e^{\frac{4c_1}{3}}-30x-25}{18(e^{\frac{4c_1}{3}}+5)}\},\{y(x)\to \frac{\sqrt{5}\sqrt{-144e^{\frac{4c_1}{3}}{x}^2-360e^{\frac{4c_1}{3}}x+24e^{\frac{8c_1}{3}}x-225e^{\frac{4c_1}{3}}+30e^{\frac{8c_1}{3}}-e^{4c_1}}+6e^{\frac{4c_1}{3}}x+15e^{\frac{4c_1}{3}}-30x-25}{18(e^{\frac{4c_1}{3}}+5)}\},\{y(x)\to \frac{-\sqrt{5}\sqrt{144e^{\frac{4c_1}{3}}{x}^2+360e^{\frac{4c_1}{3}}x+24e^{\frac{8c_1}{3}}x+225e^{\frac{4c_1}{3}}+30e^{\frac{8c_1}{3}}+e^{4c_1}}+6e^{\frac{4c_1}{3}}x+15e^{\frac{4c_1}{3}}+30x+25}{18(e^{\frac{4c_1}{3}}-5)}\},\{y(x)\to \frac{\sqrt{5}\sqrt{144e^{\frac{4c_1}{3}}{x}^2+360e^{\frac{4c_1}{3}}x+24e^{\frac{8c_1}{3}}x+225e^{\frac{4c_1}{3}}+30e^{\frac{8c_1}{3}}+e^{4c_1}}+6e^{\frac{4c_1}{3}}x+15e^{\frac{4c_1}{3}}+30x+25}{18(e^{\frac{4c_1}{3}}-5)}\}\}$$

Maple: cpu = 0.452 (sec), leaf count = 67 $$\{y\left(x\right)=\frac{(-3{\mathit{\_}\mathit{C}\mathit{1}}^2+\mathit{\_}\mathit{C}\mathit{1})x}{-3\mathit{\_}\mathit{C}\mathit{1}+1}-5\frac{{\mathit{\_}\mathit{C}\mathit{1}}^2}{-3\mathit{\_}\mathit{C}\mathit{1}+1},y\left(x\right)=\frac{x}{3}+\frac{10}{9}-\frac{2}{9}\sqrt{15x+25},y\left(x\right)=\frac{x}{3}+\frac{10}{9}+\frac{2}{9}\sqrt{15x+25}\}$$